Question

w3a4: unit 1 review
score: 40/100 answered: 10/24
question 11
solve and graph:
6x - 4 > 2x + 4 or -17 + 8x ≥ 15x + 4
-5 -4 -3 -2 -1 0 1 2 3 4 5
clear all draw:

Explanation:

Step1: Solve the first inequality

Subtract $2x$ from both sides and add 4 to both sides of $6x - 4>2x + 4$.
$6x-2x>4 + 4$, which simplifies to $4x>8$. Then divide both sides by 4, getting $x > 2$.

Step2: Solve the second inequality

Subtract $8x$ from both sides and subtract 4 from both sides of $-17 + 8x\geq15x+4$.
$-17 - 4\geq15x-8x$, which simplifies to $-21\geq7x$. Then divide both sides by 7, getting $x\leq - 3$.

Step3: Graph the solutions

For $x>2$, we use an open - circle at 2 and draw an arrow to the right. For $x\leq - 3$, we use a closed - circle at - 3 and draw an arrow to the left.

Answer:

The solution is $x\leq - 3$ or $x>2$. On the number - line, we have a closed circle at $x=-3$ with an arrow pointing left and an open circle at $x = 2$ with an arrow pointing right.